European patent publication No. 0 066 695 corresponds to U.S. Pat. No. 4,446,098 and U.S. patent application No. 268,311, filed on May 29, 1981, and discloses a spent fuel consolidation system wherein individual fuel rods can be withdrawn from a fuel element with the aid of a gripper mechanism. The gripper mechanism grasps the fuel rods at their respective longitudinal ends after the top piece and bottom piece of the fuel element have been cut therefrom. The gripper mechanism is guided over the vertically standing fuel element and includes a plurality of bores into which respective ends of the fuel rods are guided. The fuel rods are tightly clamped radially with respect to each other by means of a flexible intermediate piece disposed between two pressure plates when the latter are clamped together. The flexible intermediate member is made of plastic or rubber and is not adequately resistant or does not have a sufficiently long service life because of the radioactive radiation and the mechanical loading. The fuel rods are pulled up out of the fuel element after they are clamped. This apparatus requires a building having a sufficiently high top wall which must have a height of at least twice the length of a fuel rod. A substantial disadvantage of this arrangement is that the fuel rods must be guided into respective bores of the gripper mechanism. This can be difficult because of possible bent or deformed fuel rods, since this work must all be performed by means of remotely-manipulated equipment.